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Imagine the varying frequency generator, which feeds this frequency to the oscilloscope. Oscilloscope is turned to show signal spectra with FFT.
The image on the screen of the oscilloscope is as expected: single peak, traveling from 1 kHz to 50 kHz. Of course, my generator is not ideal, it gives a number of harmonics with less magnitude. But the strange thing happens: if my peak goes from 1 kHz to 50 kHz, the other peak appears at 50-60 kHz, and goes to lower frequencies towards mine peak. At time of appear, it's hardly noticeable, but in the end it's almost half of main frequency. Whenever varying frequency comes to it's maximum (50 kHz), ghost frequency almost approaches it. At this moment my generator drops back frequency to 1 kHz, ghost frequency disappears and process starts again.
What causes such a behaviour?

PS: I think it's more mathematical question, rather then physical or electronic.
PPS: I have some decisions, but don't want to spoil the question.

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Sounds like an aliasing phenomenon. What model oscilloscope are you using? Do you have your anti-aliasing filters on your oscilloscope turned on? – Tpofofn Dec 19 '10 at 2:34
It's very simple Textronix (TDS1000 series) it has no anti-aliasing. – PF4Public Dec 19 '10 at 4:17
@Commodore64 - definitely aliasing, you should make your comment an answer! – mtrw Dec 22 '10 at 9:06

@PF4Public, As stated in the comment and also mentioned by @mtrw this is likely aliasing phenomenon. Your intuition that it is a mathematical issue is correct. There are many websites that describe the mechanics of aliasing such as this Wikipedia article. Basically, the phenomenon occurs when an analog signal is sampled at a rate that is too slow as compared to the frequency content. You will get this phenomenon whenever the sampling frequency is less than 2x the highest frequency component (known as the Nyquist rate). When aliasing occurs, higher frequencies "appear" to be lower. Furthermore, when a signal frequency exceeds 1/2 the Nyquist rate its apparent frequency starts to go down, exactly the phenomenon that you are seeing.

To solve this problem you need to make sure that the sampling frequency of you oscilloscope is at least 2x your largest harmonic. I am not sure how the FFT function works on you oscilloscope, but sometimes the sampling rate is tied to the sec/div setting.

I hope that this helps.

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The lowest sample for your oscilloscope is 500MSps, so definitely not aliasing. Also aliasing produces multiples of base frequency, which is not the case(the phantom would increase as the fundamental increases). Try to do FFT for constant frequency signals. Also I would like to ask how fast is the signal frequency changing.

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